The 26-year-old suffered an injury-hit 2022/23 campaign and will be working to re-establish himself in the squad this summer.
Liverpool do not want to lose Diaz as they see him as a top attacker and will reject a €50 million bid from Al-Hilal.
The player has not indicated he is ready to leave the club and is unlikely to be keen to play his trade in the backwaters of the Saudi Pro League.
Diaz has taken the iconic number seven shirt at the Merseyside club, previously worn by legends such as Kevin Keegan and Kenny Dalglish.
He is the latest Liverpool target for Saudi clubs looking to strengthen their squads with players from European leagues. They are also after Fabinho and Jordan Henderson.
Fabinho did not join Liverpool in Germany for their pre-season tour. He is out of the squad as he prepares to move to Al-Ittihad.
The Saudi Pro League champions have already tabled a £40 million offer and are trying to finalise the deal.
He will join Karim Benzema, N’Golo Kante and Jota at the Saudi club once the deal is completed.
Henderson is a target for Al-Ettifaq. He will reportedly earn close to £700,000 weekly, but they have not agreed a transfer fee with Liverpool.
They want around £20m for the England international, while Al-Ettifaq have offered less than £10m.
An agreement will likely be reached, with Henderson reportedly keen to work under manager and former teammate Steven Gerrard.